Question

If six students, including two particular student $AandB$, stand in a row, then the probability that $AandB$ are separated with one student in between them is

• A. $\frac{2}{15}$
• B. $\frac{1}{5}$
• C. $\frac{4}{15}$
• D. $\frac{8}{15}$

Answer 1

The correct option is C $\frac{4}{15}$

Consider, $A,B,C$ where $C$ is between $A$ & $B$ choice for $C$ is ${}^4{C}_1,A$ & $B$ can interchange their places in $2$ ways

$A,B,C$ & other $3$ students can stand in a row in $4!$ ways. So total number of ways to stand in a row such two $A,B$ are seprated by one students in between them $=4\times 2\times 4!$

Number of ways to stand without restriction $=6!$

Probability $=\frac{4\times 2\times 4!}{6!}=\frac{4\times 2}{6\times 5}=\frac{4}{15}$